5.4. Making Surfaces. It appeared to be possible to create a surface on the edges of the weaving of Figure 24b like a soap-film. Whether this is due to the fact that the rhythm is even-even (4-4) or if this is possible with all even-even loop weavings still has to be examined. The resulting surface however is a self interwoven surface and as such a new weaving structure derived from a weaving pattern. In Figures 25 to 27 a few more examples are shown of self interwoven surfaces created from twisted loop weavings. The starting point for Figure 25 is the three way weave. In Figure 26 the Archimedean tiling (3.4.6.4) can be recognized. And to construct the surface of Figure 27 one more step was needed: starting with the Archimedean tiling (3.4.3.3.4) we first had to use the method described in section 3.1. In the surfaces the lines of the twisted ellipses can now be seen as ‘twisted holes’. In my paper “Connected Holes” [4] similar self interwoven can be found. The difference is that shape the holes now is just a twisted closed loop and not a knot, which was used as the shape of the holes in the surfaces explained in “Connected Holes”.
Figure 25a: Weave
Figure 25b: First twist
Figure 25c: Next twists
Figure 25d: Twist weave
Figure 25e: Surface
Figure 26a: Weave
Figure 26b: Surface
Figure 27a: Twist weave
Figure 27b: Surface